Mice with finitely many Woodin cardinals from optimal determinacy hypotheses

Autor:	Müller, Sandra, Schindler, Ralf, Woodin, W. Hugh
Rok vydání:	2019
Předmět:	Mathematics - Logic
Druh dokumentu:	Working Paper
Popis:	We prove the following result which is due to the third author. Let $n \geq 1$. If $\boldsymbol\Pi^1_n$ determinacy and $\Pi^1_{n+1}$ determinacy both hold true and there is no $\boldsymbol\Sigma^1_{n+2}$-definable $\omega_1$-sequence of pairwise distinct reals, then $M_n^\#$ exists and is $\omega_1$-iterable. The proof yields that $\boldsymbol\Pi^1_{n+1}$ determinacy implies that $M_n^\#(x)$ exists and is $\omega_1$-iterable for all reals $x$. A consequence is the Determinacy Transfer Theorem for arbitrary $n \geq 1$, namely the statement that $\boldsymbol\Pi^1_{n+1}$ determinacy implies $\Game^{(n)}(<\omega^2 - \boldsymbol\Pi^1_1)$ determinacy. Comment: 121 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1902.05890 Zobrazit plný text záznamu View this record from Arxiv